Low distortion frequency tracking technique

ABSTRACT

A technique for determining the characteristics of an oscillatory test signal includes acquiring a plurality of consecutive samples of a test signal. The samples are mathematically fit to a sinusoidal model, which specifies a plurality of equations. The equations have unknowns that represent characteristics of a sinusoid that substantially intersects the plurality of samples. Solving the equations for the unknowns reveals the test signal&#39;s short-term characteristics.

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] Not Applicable.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not Applicable.

REFERENCE TO MICROFICHE APPENDIX

[0003] Not Applicable

BACKGROUND OF THE INVENTION

[0004] 1. Field of the Invention

[0005] This invention relates generally to automatic test equipment,and, more particularly, to techniques employed by automatic testequipment for sampling and analyzing waveforms.

[0006] 2. Description of Related Art Including Information DisclosedUnder 37 C.F.R. 1.97 and 1.98

[0007] Automatic test equipment, or “testers,” are frequently calledupon to measure electronic signals in states of change. During theexecution of a test program for testing an electronic device, a testergenerally first applies power to the device. Then the tester applies aninput signal. After a prescribed delay, the tester samples the output ofthe device in response to the input signal. The tester then compares thesamples with expected values to determine whether the test passes orfails.

[0008] The prescribed delay between applying the input signal andsampling the output signal ensures that the output signal reaches astable state before a measurement is made. This delay is often difficultto predict, however. Therefore, test programs conventionally includedelay instructions in their software to explicitly wait fixed intervalsof time after applying an input signal, before sampling an outputsignal. To ensure that no device is measured before its output signal isready, these delay instructions tend to specify exceedingly longintervals, sometimes two or three times as long as the longest observedsettling time of the device.

[0009] Long delays excessively burden high-volume testing. Customersjudge automatic test equipment largely based upon speed of test. Timespent waiting for devices to settle is therefore particularly acute whendelays are imposed out of uncertainty, merely to provide a safetymargin.

[0010] To reduce these delays, test engineers have developed methods forsampling an output of a DUT (device under test) after the tester appliesthe input signal, and for continually testing whether the output hassettled. According to one prior technique, a tester samples the outputsignal of a DUT and repetitively performs a Discrete Fourier Transform(DFT) on successive groups of samples of the output signal. The testermonitors a characteristic of interest, for example, frequency. Once thatcharacteristic has stabilized, the test program is allowed to resume.The DFT technique therefore adapts the test program's delay to theactual settling time of the device and reduces overall delay.

[0011] This technique does not entirely eliminate unnecessary delays,however. DFTs require long computing times. Depending upon the speed ofa tester's data processing hardware, as well as the sampling rate andother factors, the tester's DFT throughput may not be able to keep pacewith the incoming data stream. Therefore, DFTs may entail unnecessarydelays. Moreover, DFTs have relatively poor frequency resolution. Thediscrete “bins” within which DFTs assign frequencies may be more widelyspaced than required. Of course, DFTs' properties can be changed toincrease frequency resolution, but this improvement is gained only atthe expense of frequency range or processing speed. In addition, DFTsgenerally require that samples be multiplied by a windowing function,such as a Hamming, Hanning, or Blackman windowing function. As known tothose skilled in the art, windowing functions introduce errors, whichfurther degrade the accuracy of the DFT technique.

[0012] Another technique has been to sample the output signal of adevice and apply linear interpolation to determine the times at whichthe output signal crosses zero (“zero” in this context refers to averageor DC value of the output signal, rather than necessarily to 0 voltsDC). The test program identifies samples on opposite sides of zero, andinterpolates between the samples to deduce the zero-crossing times.Frequency is then computed as the inverse of the difference betweenconsecutive zero-crossing times of the same slope (i.e., rising torising, or falling to falling). The zero-crossing method runs muchfaster than the DFT method—it requires only a few calculations. It alsogenerally has better frequency resolution, because it identifieszero-crossings based upon specific samples that occur at precise, knowninstants of time. Nevertheless, the zero-crossing method still suffersfrom inaccuracies, owing to the limited ability of linear interpolationto accurately identify the zero-crossings of inherently non-linearsinusoids.

[0013] What is needed is a more accurate, high-speed technique fordetermining the characteristics of a test signal as a function of time.

BRIEF SUMMARY OF THE INVENTION

[0014] With the foregoing background in mind, it is an object of theinvention to determine, quickly and accurately, the characteristics ofan oscillatory test signal.

[0015] To achieve the foregoing object, as well as other objectives andadvantages, a technique for determining the characteristics of anoscillatory test signal includes acquiring a plurality of consecutivesamples of a test signal. The method includes mathematically fitting asinusoidal model to the samples. The sinusoidal model specifies aplurality of equations having unknowns that represent characteristics ofan ideal sinusoid that substantially intersects the plurality ofsamples. Solving for the unknowns reveals the test signal'scharacteristics.

[0016] According to one aspect of the invention, a tester applies thetechnique for determining when a test signal from a device under testhas settled. The tester repetitively samples the test signal, appliesthe model, and solves for at least one of the test signal'scharacteristics. When, over the course of multiple iterations, the testsignal is found to stabilize, the test program can safely advance,without wasting valuable test time.

[0017] According to another aspect of the invention, a tester appliesthe above-described technique for characterizing a transient response ofa test signal. According to this variation, a test program induces achange in a device under test, and monitors the test signal over timeusing the technique. The test program ascertains the output's responseto the change by referring to the test signal's characteristics asreported by the technique over time.

[0018] According to yet another aspect of the invention, a testerapplies the above-described technique for characterizing afrequency-modulated or phase-modulated test signal. The frequency of thetest signal can be directly reported, on a cycle-by-cycle basis.Alternatively, the frequency of the test signal can be integrated withrespect to time to provide a measure of phase, or phase can be computeddirectly.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0019] Additional objects, advantages, and novel features of theinvention will become apparent from a consideration of the ensuingdescription and drawings, in which—

[0020]FIG. 1 is a graph of frequency versus sample number for anoscillatory test signal, wherein the displayed frequencies are computedusing a Discrete Fourier Transform (DFT) technique according to theprior art;

[0021]FIG. 2 is a graph of frequency versus sample number for theoscillatory test signal upon which FIG. 1 is based, wherein thefrequencies are computed using a zero-crossing technique according tothe prior art;

[0022]FIG. 3 is a graph of frequency versus sample number for theoscillatory test signal upon which FIGS. 1 and 2 are based, wherein thefrequencies are computed in accordance with the invention;

[0023]FIG. 4 is a software listing showing module-level definitions anda main routine for comparing results of different techniques forestimating the frequency of an oscillatory test signal;

[0024]FIGS. 5A and 5B are software listings of the DFT technique used togenerate the graph of FIG. 1;

[0025]FIG. 6 is a software listing of the zero-crossing technique usedto generate the graph of FIG. 2;

[0026]FIG. 7 is an example of a software listing of a techniqueaccording to the invention for generating the graph of FIG. 3;

[0027]FIG. 8 is a flowchart showing a process according to the inventionfor testing a device that has an indeterminate settling time;

[0028]FIG. 9 is a highly simplified block diagram of a test system inwhich the process of FIG. 8 can be performed; and

[0029]FIG. 10 is a plot of frequency and phase of a modulated testsignal, which can be examined according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0030] An oscillatory test signal, even one whose characteristics changeover time, can be regarded as having constant characteristics in theshort-term, even if only for a single group of samples. We haverecognized that the short-term characteristics of an oscillatory testsignal can be mathematically modeled as an idealized sinusoid:

x _(n) =A cos(nα+β)+B.  (EQ. 1)

[0031] In EQ. 1, “x_(n)” represents the value of an n^(th) sample of thetest signal. “A” corresponds to test signal's amplitude, B correspondsto its DC offset, a corresponds to its frequency, and β corresponds itsphase. A measurement circuit such as a digitizing sampler can directlymeasure each sample x_(n). By measuring four consecutive, uniformlyspaced samples (e.g., x₀ to x₃), one can construct four equations infour unknowns, as follows:

x ₀ =A cos(β)+B  (EQ. 2)

x ₁ =A cos(α+β)+B  (EQ. 3)

x ₂ =A cos(2α+β)+B  (EQ. 4)

x ₃ =A cos(3α+β)+B  (EQ. 5)

[0032] One can solve for the four unknowns, A, B, α, and β, to fit theidealized sinusoid of EQ. 1 to the samples as follows. First, one caneliminate the DC offset, B, by subtracting adjacent datapoints:

y ₀ =x ₁ −x ₀ =A[cos(α+β)−cos(β)]  (EQ. 6)

y ₁ =x ₂ −x ₁ =A[cos(2α+β)−cos(α+β)]  (EQ. 7)

y ₂ =x ₃ −x ₂ =A[cos (3α+β)−cos(2α+β)]  (EQ. 8)

[0033] Next, one can introduce the following simplifying relation:

cos((n+1)α+β)−cos(nα+β)=2|sin(α/2)|cos(nα+β+atan2(sin α,cos(α−1))),  (EQ. 9)

[0034] wherein atan2(x, y) equals atan(x, y) for x>=0, and equalsπ+atan(x, y) for x<0. One can derive the relation of EQ. 9 as follows:$\begin{matrix}{{{\cos \quad \left( {{\left( {n + 1} \right)\alpha} + \beta} \right)} - {\cos \left( {{n\quad \alpha} + \beta} \right)}} = \quad {{\cos \left( {\alpha + {n\quad \alpha} + \beta} \right)} - {\cos \left( {{n\quad \alpha} + \beta} \right)}}} \\{= \quad {{{\cos (\alpha)}{\cos \left( {{n\quad \alpha} + \beta} \right)}} -}} \\{\quad {{{\sin (\alpha)}{\sin \left( {{n\quad \alpha} + \beta} \right)}} - {\cos \left( {{n\quad \alpha} + \beta} \right)}}} \\{= \quad {{\left( {{\cos (\alpha)} - 1} \right){\cos \left( {{n\quad \alpha} + \beta} \right)}} -}} \\{\quad {{\sin (\alpha)}{\sin \left( {{n\quad \alpha} + \beta} \right)}}} \\{= \quad {{SQRT}\left( {\left( {{\cos (\alpha)} - 1} \right)^{2} +} \right.}} \\{{\quad \left. {\sin^{2}(\alpha)} \right)}\left\lbrack {\left( {{\cos (\alpha)} - 1} \right){\cos \left( {{n\quad \alpha} + \beta} \right)}/} \right.} \\{\quad {{SQRT}\left( {\left( {{\cos (\alpha)} - 1} \right)^{2} +} \right.}} \\{{\quad \left. {\sin^{2}(\alpha)} \right)} - {{\sin (\alpha)}{\sin \left( {{n\quad \alpha} + \beta} \right)}/}} \\{\quad \left. {{SQRT}\left( {\left( {{\cos (\alpha)} - 1} \right)^{2} + {\sin^{2}(\alpha)}} \right)} \right\rbrack} \\{= \quad {{SQRT}\left( {\left( {{\cos (\alpha)} - 1} \right)^{2} +} \right.}} \\{{\quad \left. {\sin^{2}(\alpha)} \right)}*{\cos\left( {{n\quad \alpha} + \beta +} \right.}} \\{\quad \left. {a\quad \tan \quad 2\left( {{\sin \quad \alpha},{\cos \left( {\alpha - 1} \right)}} \right)} \right)} \\{= \quad {{{SQRT}\left( {{\cos^{2}(\alpha)} - {2\quad {\cos (\alpha)}} + 1} \right)} +}} \\{{\quad \left. {\sin^{2}(\alpha)} \right)}*{\cos\left( {{n\quad \alpha} + \beta +} \right.}} \\{\quad \left. {a\quad \tan \quad 2\left( {{\sin \quad a},{\cos \left( {\alpha - 1} \right)}} \right)} \right)} \\{= \quad {{{SQRT}\left( {2 - {2\quad {\cos (\alpha)}}} \right)}*{\cos\left( {{n\quad \alpha} + \beta +} \right.}}} \\{\quad \left. {a\quad \tan \quad 2\quad \left( {{\sin \quad \alpha},{\cos \left( {\alpha - 1} \right)}} \right)} \right)} \\{= \quad {2{{SQRT}\left( {\frac{1}{2} - {\frac{1}{2}{\cos (\alpha)}}} \right)}*{\cos\left( {{n\quad \alpha} + \beta +} \right.}}} \\{\quad \left. {a\quad \tan \quad 2\left( {{\sin \quad \alpha},{\cos \left( {\alpha - 1} \right)}} \right)} \right)} \\{= \quad {2{{\sin \left( {\alpha/2} \right)}}*{\cos\left( {{n\quad \alpha} + \beta +} \right.}}} \\{\quad \left. {a\quad \tan \quad 2\left( {{\sin \quad \alpha},{\cos \left( {\alpha - 1} \right)}} \right)} \right)}\end{matrix}$

[0035] One can now substitute EQ. 9 into EQS. 6-8 to yield—

y ₀ =x ₁ −x ₀=2A|sin(α/2)|cos(β+atan2(sin α, cos(α−1)))

y ₁ =x ₂ −x ₁=2A|sin(α/2)|cos(α+β+atan2(sin α, cos(α−1)))

y ₂ =x ₃ −x ₂=2A|sin(α/2)|cos(2α+β+atan2(sin α, cos(α−1)))

[0036] which can be rewritten as—

y ₀ =x ₁ −x ₀=2A|sin(α/2)|cos(−α+αβ+atan2(sin α, cos(α−1)))

y ₁ =x ₂ −x ₁=2A|sin(α/2)|cos(α+β+atan2(sin α, cos(α−1)))

y ₂ =x ₃ −x ₂=2A|sin(α/2)|cos(α+αβ+atan2(sin α, cos(α−1)))

[0037] Letting γ=α+β+atan2(sin α, cos(α−1)) enables furthersimplifications:

y ₀ =x ₁ −x ₀=2A|sin(α/2)|cos(−α+γ)  (EQ. 10)

y ₁ =x ₂ −x ₁=2A|sin(α/2)|cos(γ)  (EQ. 11)

y ₂ =x ₃ −x ₂=2A|sin(α/2)|cos(α+γ)  (EQ. 12)

[0038] Combining EQS. 10-12 eliminates all variables except α:$\begin{matrix}{{\left( {y_{0} + y_{2}} \right)/y_{1}} = \quad {2\quad {{A\left\lbrack {{{{\sin \left( {\alpha/2} \right)}}{\cos \left( {{- \alpha} + \gamma} \right)}} + {\cos \left( {\alpha + \gamma} \right)}} \right\rbrack}/}}} \\{\quad \left\lbrack {2A{{\sin \left( {\alpha/2} \right)}}{\cos (\gamma)}} \right\rbrack} \\{= \quad {\left( {{\cos \left( {{- \alpha} + \gamma} \right)} + {\cos \left( {\alpha + \gamma} \right)}} \right)/{\cos (\gamma)}}} \\{= \quad \left( {{{\cos (\alpha)}{\cos (\gamma)}} + {{\sin (\alpha)}{\sin (\gamma)}} + {{\cos (\alpha)}{\cos (\gamma)}} -} \right.} \\{{\quad \left. {{\sin (\alpha)}{\sin (\gamma)}} \right)}/{\cos (\gamma)}} \\{= \quad {2{\cos (\alpha)}{{\cos (\gamma)}/{\cos (\gamma)}}}} \\{= \quad {2{\cos (\alpha)}}}\end{matrix}$

[0039] Applying EQS. 6-8 allows one to solve for α:

α=a cos((y ₀ +y ₂)/2y ₁)=a cos(x₃ −x ₂)−(x ₁ −x ₀))/(2(x ₂ −x ₁)).  (EQ.13)

[0040] The frequency (in Hz) of the test signal can then be computed as2πα.

[0041] One can solve EQS. 2-5 for each of the other unknowns. To solvefor the phase of the sinusoid, β, one can divide y₁ (EQ. 7) by y₀ (EQ.6): $\begin{matrix}{{y_{1}/y_{0}} = \quad {\left\lbrack {{\cos \left( {{2\quad \alpha} + \beta} \right)} - {\cos \left( {\alpha + \beta} \right)}} \right\rbrack/\left\lbrack {{\cos \left( {\alpha + \beta} \right)} - {\cos (\beta)}} \right\rbrack}} \\{= \quad {\left\lbrack {{\cos \quad 2\alpha \quad \cos \quad \beta} - {\sin \quad 2\quad \alpha \quad \sin \quad \beta} - {\cos \quad \alpha \quad \cos \quad \beta} + {\sin \quad \alpha \quad \sin \quad \beta}} \right\rbrack/}} \\{\quad \left\lbrack {{\cos \quad \alpha \quad \cos \quad \beta} - {\sin \quad \alpha \quad \sin \quad \beta} - {\cos \quad \beta}} \right\rbrack} \\{= \quad {\left\lbrack {{\left( {{\cos \quad 2\quad \alpha} - {\cos \quad \alpha}} \right)\cos \quad \beta} - {\left( {{\sin \quad 2\alpha} - {\sin \quad \alpha}} \right)\sin \quad \beta}} \right\rbrack/}} \\{\quad \left\lbrack {{\left( {{\cos \quad \alpha} - 1} \right)\cos \quad \beta} - {\sin \quad \alpha \quad \sin \quad \beta}} \right\rbrack}\end{matrix}$

[0042] Cross-multiplying and collecting terms including β yields:

[y ₁(cos α−1)−y ₀(cos 2a−cos α)]cos β=[y ₁ sin α−y ₀(sin 2α−sin α)]sinβ.

[0043] Therefore,

β=atan{[y ₁(cos α−1)−y ₀(cos 2α−cos α)]/[y ₁ sin α−y ₀(sin 2α−sinα)]}.  (EQ. 14)

[0044] Except for the atan operation, all trigonometric computations canbe avoided by employing the following identities:

cos α=(y ₀ +y ₂)/2y ₁=((x ₃ −x ₂)−(x ₁ −x ₀))/(2(x ₂ −x ₁))

cos 2α=2 cos²α−1

sin α=SQRT(1−cos²α)

sin 2α=2 sin α cos α.

y ₀ =x ₁ −x ₀

y ₁ =x ₂ −x ₁

[0045] One can also solve for the amplitude A of the sinusoid using EQ.6:

A=y ₀/[cos(α+β)−cos(β)]=y ₀/[cos(α+β)−cos(β)].  (EQ. 15)

[0046] Finally, one can solve for DC offset B using EQ. 2:

B=A cos(β)−x ₀  (EQ. 16)

[0047] This “sinusoidal fit” technique can estimate the frequency of atest signal much more quickly than the DFT method. It requires only onetrigonometric operation and several arithmetic operations. Although itscomputational requirements are on the same order as the zero-crossingtechnique's, the sinusoidal fit technique is more accurate because itavoids errors in linear interpolation. Because it fits the samples to asinusoid, not to a straight line, the sinusoidal fit technique moreclosely estimates the oscillatory behavior of the test signal.

[0048] To prevent aliasing, the test signal should be sampled at a ratethat equals or exceeds the Nyquist rate of the test signal. Preferably,the four samples x₀−x₃ should fall within a single period of the testsignal. This is not strictly required, however. Frequencies can beaccurately deduced for a wide range of sampling intervals. In a typicaltesting application, the frequency of a test signal is approximatelyknown in advance. By specifying the sampling rate of the digitizer basedon the expected frequency of the test signal, the range over which thesinusoidal fit technique operates accurately will generally be wideenough to encompass the normal frequency variations of the test signal.

[0049] FIGS. 1-3 show the results of three different frequencyestimating techniques operating on the same data set. The data set wasacquired by sampling the output of a voltage-controlled oscillator (VCO)at a rate of 20.48 MHz, as the VCO responds to power being applied toits power supply terminals. FIG. 1 shows the DFT technique, FIG. 2 showsthe zero-crossing technique, and FIG. 3 shows the sinusoidal fittechnique. FIGS. 4-7 show listings of the software used to generate thegraphs of FIGS. 1-3.

[0050] The frequency reported by the sinusoidal fit technique hasnotably lower noise than the other two methods. The lower noise derivesfrom the fact that the technique yields more accurate results than thealternatives. Noise remains low even though test signal's frequencyvaries by a factor of three.

[0051] Numerous advantages derive from lower noise. Lower noise allows atest program to determine quickly when a test signal has settled,without the need for additional averaging or delays. It also enables oneto examine nuances in the test signal's settling characteristics, whichotherwise might be concealed. For example, the sinusoidal fit techniquereveals, more sharply than the other methods, a periodic component 310in the settling characteristic of the VCO.

[0052]FIG. 8 shows a process for using the sinusoidal fit technique todetermine when a test signal has settled. This method is preferablyperformed by a test program running on an automatic test system. FIG. 9shows a highly simplified diagram of an automatic test system 910. Theautomatic test system 910 includes a test computer 912, a power supply914, a sourcing circuit 916, and a measurement circuit 918. According tothe method, the tester 910 applies power to a DUT 920 (step 810).Depending upon the type of device, the tester may also apply an inputsignal to the DUT (step 812). If the DUT is a VCO, for example, thedevice requires a separate input signal for establishing an outputfrequency. If the device is a fixed oscillator or similar device,however, no separate input signal is needed, in which case step 812 maybe omitted.

[0053] According to this technique, the sinusoidal fit technique can becommenced at any time before the output signal is expected to havesettled. Steps 814-816 show a single iteration of this technique. Themeasurement circuit 918 obtains four consecutive samples from the outputof the DUT (step 814). The test computer 912 fits the samples to asinusoidal model (step 816) by solving the model's equations forfrequency. Upon completion of step 816, a single frequency point isestablished. The test program then repeats the sinusoidal fit techniqueuntil the frequencies reach a stable value. Once stability is attained,the test program can proceed (step 820).

[0054] The particular requirements of a test dictate the manner in whichthe sinusoidal fit technique progresses through the sampled data. If adevice is expected to settle quickly, then the technique shouldpreferably be repeated at a high rate. At the limit, the technique canbe performed once for every sample. For instance, the technique canfirst be performed on samples x₀, x₁, x₂, and X₃, then on samples, x₁,x₂, x₃, and x₄, then on samples x₂, x₃, x₄, and x₅, and so on. If,however, the device is expected settle slowly, then the technique can berepeated less often, for example, once every 100 samples.

[0055] Testing requirements also dictate when the test signal is deemedto have settled. Typically, the test program stores a frequency “window”having a high limit and a low limit. The test signal is deemed to havesettled when its frequency remains within the window for a designatedperiod of time. This is merely an example, however. The specific mannerin which the test signal is deemed to have settled is not critical tothe invention.

[0056] The tester's computer may operate in connection with digitalsignal processing hardware. This may include specialized circuits or oneor more auxiliary processors that communicate with the test computer toincrease throughput.

[0057] Alternatives

[0058] Having described one embodiment, numerous alternative embodimentsor variations can be made. As described herein, consecutive samples areused to estimate the test signal's characteristics. However, a testercan instead sample the test signal at a high sampling rate and examineonly a regularly spaced fraction of the samples taken. Examining everytenth sample is equivalent to examining consecutive samples at one-tenththe sampling rate. The invention is not limited, therefore, to strictlyconsecutive samples.

[0059] The sinusoidal fit technique can also be used in connection withsample rate conversion. As known to those skilled in the art, samplerate conversion maps actual samples of a signal taken with one samplingclock to synthesized samples referenced to a different sampling clock.Sample rate conversion is especially useful in this context forexamining non-uniformly sampled test signals. Using sample rateconversion, samples that are non-uniformly spaced but have preciselyknown timing can be converted into regularly spaced samples, which areamenable to the sinusoidal fit technique described herein.

[0060] In addition, analog or digital filters can be applied to the testsignal, prior to processing by the sinusoidal fit technique. Thesinusoidal fit technique can also incorporate digital filtering in itscomputations, if desired, to eliminate the need for multiple filteringstages.

[0061] The sinusoidal fit technique has been shown and described hereinfor determining when a device under test settles. This is merely one ofmany possible applications, however. Another area in which the techniquecan be used is for examining the response characteristics of a testsignal. For instance, the technique can examine the frequency changes atthe output of a VCO as it responds to an input voltage step. It can alsoexamine the frequency noise on a test signal, or transient effectscaused by a variety of circuit disturbances.

[0062] The technique is also useful for testing telecommunicationsdevices, such as those that employ frequency modulation or phasemodulation. Because the sinusoidal fit technique has low noise and canbe updated on a cycle-to-cycle basis (or more frequently), it can beused for examining modulated signals carried on these devices. Forexample, a test system can capture the output of a modulatingtransmitter and examine its characteristics. FIG. 10 shows a plot of amodulated test signal 1010 and its frequency 1012 as a function of time.In addition to determining frequency, the sinusoidal fit technique canalso determine the relative phase of the test signal. One way ofdetermining relative phase is by integrating the frequency values thetechnique produces with respect to time. As is known, phase ismathematically the integral of frequency. Using numerical techniques,phase can be computed by adding (accumulating) each new frequency valuewith the sum of all previous values. The function 1014 represents thenormalized phase of the test signal 1010. Because phase continues togrow as frequencies accumulate, phase is more easily observed by firstsubtracting, or normalizing, the center frequency of the modulated testsignal from each frequency value, before accumulating the frequencyvalue with its predecessors. The normalized phase function, known in theart as a “phase plot,” therefore reveals changes in phase from normal.For example, portion 1016 represents a region where phase is increasingrelative to normal; portion 1018 represents a region where phase isdecreasing relative to normal. A test program can analyze these changesto determine whether a modulating transmitter is properly and accuratelygenerating the modulated test signal.

[0063] Each of these alternatives and variations, as well as others, hasbeen contemplated by the inventor and is intended to fall within thescope of the instant invention. It should be understood, therefore, thatthe foregoing description is by way of example, and the invention shouldbe limited only by the spirit and scope of the appended claims.

What is claimed is:
 1. In an automatic system for testing electroniccomponents, a method for determining the characteristics of anoscillatory test signal produced by a device under test, comprising: (A)acquiring a plurality of samples of the test signal; (B) mathematicallyfitting a sinusoidal model to the samples, the sinusoidal modelspecifying a plurality of equations having unknowns representingcharacteristics of a sinusoidal signal that substantially intersects theplurality of samples; and (C) solving the plurality of equations for atleast one of the unknowns to reveal at least one characteristic of thetest signal.
 2. A method as recited in claim 1, wherein each of theplurality of equations is substantially of the form x_(n)=A cos(nα+β)+B,wherein “x_(n)” is the n^(th) sample, “A” corresponds to amplitude, Bcorresponds to DC offset, α corresponds to frequency, and β correspondsto phase of the sinusoidal signal specified by the model.
 3. A method asrecited in claim 1, wherein the plurality of samples is four samplesevenly distributed in time.
 4. A method as recited in claim 3, whereinthe plurality of samples is acquired at a sampling rate as least as fastas the Nyquist rate of the test signal.
 5. A method as recited in claim1, further comprising repetitively performing steps A-C for differentpluralities of samples while monitoring the at least one characteristicof the test signal.
 6. A method as recited in claim 5, furthercomprising determining when the at least one characteristic of the testsignal has settled to a stable value.
 7. A method as recited in claim 5,further comprising storing the at least one characteristic as a functionof time.
 8. A method as recited in claim 7, further comprisingdisplaying the at least one characteristic as a function of time.
 9. Amethod as recited in claim 1, wherein the at least one characteristic ofthe test signal is frequency.
 10. A method as recited in claim 9,further comprising accumulating frequency measurements of the testsignal to generate an indication of phase of the test signal.
 11. Amethod as recited in claim 10, wherein the device under test is atransmitting device that encodes data using one of phase modulation andfrequency modulation, and further comprising monitoring the at least onecharacteristic of the test signal to determine whether the transmittingdevice accurately modulates data.
 12. A method as recited in claim 1,wherein the device under test is a transmitting device that encodes datausing one of phase modulation and frequency modulation, and furthercomprising monitoring the at least one characteristic of the test signalto determine whether the transmitting device accurately modulates data.13. A method of testing a device to determine whether it is operatingproperly, comprising: (A) applying power to the device; (B) waiting foran output signal from the device to settle, including— (i) sampling theoutput signal from the device, (ii) mathematically fitting a sinusoidalmodel to the samples, the sinusoidal model specifying a plurality ofequations having unknowns representing characteristics of an idealsinusoid substantially intersecting the plurality of samples, (iv)solving the plurality of equations for at least one of the unknowns toreveal at least one characteristic of the test signal, and (v) repeatingsteps i-iv until the at least one characteristic of the test signalsettles; and (C) resuming testing activities, upon the completion ofstep (B).
 14. A method as recited in claim 13, wherein the testingactivities comprise: measuring a characteristic of the device undertest; and comparing the measured characteristic with at least oneexpected value to determine whether the device passes or fails.
 15. Amethod as recited in claim 13, controlled by a test program running onan automatic test system for testing electronic devices.
 16. A method asrecited in claim 15, further comprising production testing devices undertest.
 17. A method for testing a device to determine whether it isoperating properly, comprising: (A) inducing a transient in the device;(B) monitoring the response of the device to the transient, including—(i) sampling the output signal from the device, (ii) mathematicallyfitting a sinusoidal model to the samples, the sinusoidal modelspecifying a plurality of equations having unknowns representingcharacteristics of an ideal sinusoid substantially intersecting theplurality of samples, (iv) solving the plurality of equations for atleast one of the unknowns to reveal at least one characteristic of thetest signal, and (v) repeating steps i-iv to track the at least onecharacteristic as a function of time; and (C) comparing the at least onecharacteristic with at least one expected value, to determine whetherthe device passes or fails.
 18. A method as recited in claim 17, furthercomprising displaying, for visual examination, the at least onecharacteristic as a function of time.
 19. A method as recited in claim17, performed by an automatic test system for testing electronicdevices.
 20. An automatic system for testing electronic components,comprising: a measurement circuit for acquiring samples from an outputsignal of a device under test; and processing means for running a testprogram for testing the device under test, including— means formathematically fitting a sinusoidal model to the samples, the sinusoidalmodel specifying a plurality of equations having unknowns representingcharacteristics of an ideal sinusoid substantially intersecting theplurality of samples, means for solving the plurality of equations forat least one of the unknowns to reveal at least one characteristic ofthe test signal, and means for repetitively operating the means formathematically fitting and the means for solving to ascertain changes inthe at least one characteristic as a function of time.
 21. An automatictest system as recited in claim 20, wherein the processing meanscomprises a test computer.
 22. An automatic test system as recited inclaim 21, wherein the processing means further comprises Digital SignalProcessing (DSP) hardware.
 23. An automatic test system as recited inclaim 20, further comprising: at least one power supply for applyingpower to the device under test; and at least one stimulus circuit forapplying an input signal to the device under test.
 24. An automatic testsystem as recited in claim 20, wherein each of the plurality ofequations is substantially of the form x_(n)=A cos(nα+β)+B, wherein“x_(n)” is the n^(th) sample, “A” corresponds to amplitude, Bcorresponds to DC offset, α corresponds to frequency, and β correspondsto phase.